African Americans and Hispanic/Latinos - two of the largest minority groups in the U.S. - are admixed populations with ancestry from multiple ancestral populations. This proposal outlines several population genetic methods using admixed populations that will facilitate medical genetics. The first proposed method seeks to improve estimation of the time course of admixture of Africans and Europeans giving rise to African American populations. Delineating the waves of migration in the admixture will improve understanding of the complex structure of African Americans and may provide insights into how to better the design of admixture studies that may boost power to detect variants associated with disease. The second proposed method will leverage sequence data to fine map ancestry breakpoints in local ancestry estimation of admixed individuals. This method can lead to an increased resolution of ancestry, and can extend local ancestry estimation to populations with older admixture, increasing the number of populations that can be utilized for admixture mapping. It may also allow the construction of a fine- scale human genetic map without family or pedigree data. The third method outlined in this proposal will examine the health impact of variants introduced into modern human populations through ancient admixture. The new genetic variants introduced by gene flow, from one population into another, have the potential to be adaptive or to have an impact on traits. This aim of the proposal will explore whether ancient admixture introduced variants that have undergone positive selection or that are associated with height, weight, or disease. In particular, this proposal will examine the recently discovered gene flow from Neandertals into non-African populations, to examine whether the highly-diverged Neandertal variants were adaptive and have undergone positive selection, or whether these variants are associated with morphometric phenotypes or disease.